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On the completeness of the system \(\{z^{\tau_n}\}\) in \(L^{2}\). (English) Zbl 1014.30004

Summary: Given an unbounded domain \(\Omega\) located outside an angle domain with vertex at the origin, and a sequence of distinct complex numbers \(\{\tau_n\}\) \((n=1,2,\dots)\) satisfying \({n\over|\tau_n|} \to D\) as \(n\to\infty\) with \(0<D<\infty\), and \(|\arg (\tau_n)|<\alpha< {\pi\over 2}\), we obtain a completeness theorem for the system \(\{z^{\tau_n}\}\) \((n=1,2, \dots)\) in \(L^2_a[\Omega]\). The case with weight is also considered.

MSC:

30B60 Completeness problems, closure of a system of functions of one complex variable
42C30 Completeness of sets of functions in nontrigonometric harmonic analysis
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References:

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